The Stokes parameters and the linear polarization $P_1$ of small rough particles composed of ice and silicate are studied with statistical methods. The probability density function of $P_1$ and a regression analysis for the first two Stokes parameter $I_s^2$ and $Q_s^2$ are presented for three typical scattering angles $\theta_s$=60\degres, 90\degres and 150\degres. The width of the probability density function of $P_1$ given by its standard deviation increases with the roughness of the particles. A linear relationship between $I_s^2$ and $Q_s^2$ is found by the regression analysis. The slope of the linear mode reflects the correlation between $I_s^2$ and $Q_s^2$ that, for a specific composition of the particles, depends on the roughness of the particles and the scattering angles. The value of the constant of the linear regression is characteristic of the composition of the particles and is not sensitive to the roughness of the particles and the scattering angles. The scattering angle $\theta_s$=150\degres is the most appropriate angle for a study of rough particles of different composition.